Answer:
θ = 0 to θ = 2π, r = 1 to r = -1 and z = 0 to z = 3
Step-by-step explanation:
Since the integration is in cylindrical coordinates, θ is integrated from 0 to 2π.
Since r = cosθ
when θ = 0, r = cos0 = 1
when θ = 2π, r = cos2π = -1
Since the region is bounded below by the plane z = 0, and on the top by the paraboloid z = 3r², z is integrated from z = 0 to z = 3r².
So, when r = 1, z = 3r² = 3(1)² = 3
when r = -1, z = 3r² = 3(-1)² = 3
So, the limits of integration of
∭f(r,θ,z)dz r dr dθ are θ = 0 to θ = 2π, r = 1 to r = -1 and z = 0 to z = 3
